Brent explained on Tuesday how to easily tell if a number is divisible by six. There's a good way to tell also, if a number is divisible by nine: Add all the digits up, and if the sum of the digits is divisible by nine, then the number is divisible by nine too. So if you have a very large number, like 891,245? Is it divisible by nine?

Is 891,245 divisible by 9?

8+9+1+2+4+5 = 29

Is 29 divisible by 9? Nope, so:

891,245 is not divisible by 9.

But what if you have a really big number? Well here's a cool trick: You can get recursive. If the sum of the digits is too big to figure out in your head if it's divisible by nine, you can add the sum of the digits of the sum of the digits, and see whether that's divisible by nine. Here's an example::

Is 578,459,126,354,851,649,325,124,878,990,003 divisible by 9?

Sum of digits: 153 I don't know off the top of my head if 153 is divisible by 9, so I'll sum the digits again:

1+5+3 = 9

Is 9 divisible by 9? Of course it is, so:

578,459,126,354,851,649,325,124,878,990,003 is divisible by 9.

Guess what — it works for 3 too. Oh, and by the way, 153 divided by 9 is 17.

Dave wrote, “The Web is so much faster that it makes relational writing possible, much the same way that outlining software made outlining possible. (Before that many people faked the outlines, we were supposed to create them before writing the paper, but instead we wrote them after.)”

I told Dave a couple of weeks ago (in an outline) that someday I’d tell him why I used to absolutely hate outlines, so here it is:

In the winter of 1978 or maybe ’79, I was in the fourth grade, at Arrowhead Elementary School in Shawnee Mission, KS. My social studies teacher wanted to teach us how to make outlines. First, she taught us the part that, at the time, I thought was most interesting – the numbering system. Top-level headings have big Roman numerals. Second-level headings are capital letters of the alphabet, third-level are lower-case Roman numerals, fourth are lower-case letters, etc. Each heading should contain a single idea, not more than one or two sentences.

This made a lot of sense to me intuitively. Break ideas up into neat little chunks which are easy to process. If you need more detail than fits in a single heading, break the idea up further, and start a subordinate outline underneath the current heading. Recurse until done. It seemed like it could be a really useful strategy for organizing complex ideas. (Plus I liked the way the numbering worked, and I was big-into numbers in general.)

Then my teacher did something that made me hate outlines for years after that. In fact I hated outlines until I saw ThinkTank on my dad’s IBM PC, the summer after the eighth grade. What she did was this: She picked a chapter in our social studies text, and asked us to read it, and then make an outline of it. That may sound like a pretty innocuous assignment, but after I thought about it for a second, it really made me upset, for two reasons:

1) I’d have rather had a more creative assignment where we got to make an outline of some of our own ideas, and not to re-do a bunch of work that the authors of the text had already done. They probably did it better than I would anyway, since I didn’t much like reading that text in the first place.

2) Wait a minute, there’s already an outline of the chapter in the damn table of contents! It was right there, with the numerals, indenting, and everything. Was I supposed to just copy the table of contents out of the front of the text? That would have been a pretty dumb assignment. If not then why was she telling us we had to do this redundant work?

So I raised my hand, and asked her, “Why do I have to make an outline of this chapter when there already is one in the table of contents?” As other students started flipping to the front of their books to look at the prior art, she glared at me and said, “just do what I tell you to do.” Well that set me off.

Not only was she asking me to do something that I thought was stupid, she wouldn’t even tell me why. So what did I do? I told her no; I would not make an outline, unless she told me why. The thing is, I don’t think she knew why. Anyway, what ensued was the second biggest conflict I ever had with a teacher, the details of which aren’t too interesting. What is interesting is the parent-teacher conference that came out of it.

I don’t remember if it was the same day, or the next day, but after school, my mom arrived, and they went into the classroom, asked me to wait outside, and closed the door. After about ten minutes of muffled conversation, I heard my teacher scream at her, “Jacob is just like you: he’ll never amount to anything!!” Boy, was that ever the wrong thing to say to the wrong person. My mom, at that time a teaching Nephrologist and leader of her own research group at the University of Kansas Medical Center in Kansas City, MO, erupted at my teacher with a force that I’ve only witnessed from her a few times in my life. A few minutes later, I had to stop listening; it wasn’t a fair fight.

I walked down the hall toward the drinking fountain, sat on the floor, and occupied myself with playing with my LED-digital watch, while waiting for the door to open. Eventually it did. My mom emerged. My teacher did not. We went home. Mrs. Watson never asked me to make another outline.

Nowadays I live in outlines. I use them to write, to communicate, to program, to organize, to take notes…

Oh, and one other thing: I actually did make outlines for most of the papers I wrote in high school and college, before I wrote the paper. ;->6:11:52 PM

Wired: Computer Optics Not an Illusion. “Photonic crystals, which use photons instead of electrons as the marker for representing digital 0s and 1s, promises both reduced sizes and drastically increased computing speeds.”